Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends.
When we're adding and subtracting, do evens make odds into evens? Do odds make evens odd? Which one has… more power!?
The commutative and associative properties are a whole lot more interesting when you apply them to a mathematical operation that you created!
Say you have a dollar. Say you can double that dollar each day: $1, $2, $4, and so on. How long will it take to reach… one million dollars? Not as long as you might think!